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A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors…
The recently introduced backward Monte-Carlo method [Johan Carlsson, arXiv:math.NA/0010118] is validated, benchmarked, and compared to the conventional, forward Monte-Carlo method by analyzing the error in the Monte-Carlo solutions to a…
The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of…
The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control…
Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down in their convergence to a value. While solving the sign problem is generically…
Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical…
We introduce a Monte Carlo scheme for sampling bold-line diagrammatic series specifying an unknown function in terms of itself. The range of convergence of this bold(-line) diagrammatic Monte Carlo (BMC) is significantly broader than that…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
We study random compressible viscous magnetohydrodynamic flows. Combining the Monte Carlo method with a deterministic finite volume method we solve the random system numerically. Quantitative error estimates including statistical and…
Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…
We present a real-time quantum Monte Carlo algorithm that simulates the dynamics of open quantum systems by stochastically compressing and evolving the density matrix under both Markovian and non-Markovian master equations. Our algorithm…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
We present a new Monte Carlo algorithm for simulating quantum spin systems which is able to suppress the negative sign problem. This algorithm has only a linear complexity in the lattice size used for the simulation. A general description…
Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…
We present two diagrammatic Monte Carlo methods for quantum systems coupled with harmonic baths, whose dynamics are described by integro-differential equations. The first approach can be considered as a reformulation of Dyson series, and…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
Diagrammatic Monte Carlo (DiagMC) is a numeric technique that allows one to calculate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem that is…
The notorious sign problem severely limits the applicability of quantum Monte Carlo (QMC) simulations, as statistical errors grow exponentially with system size and inverse temperature. A recent proposal of a quantum-computing stochastic…